Advanced multimedia services continue to drive requirements for increasing data rates and higher performance in wireless systems Current technologies for high performance communication systems, such as those specified by the European terrestrial digital video broadcasting (DVB-T) standard, the Japanese integrated services digital broadcasting terrestrial standard (ISDB-T) and the digital audio broadcasting (DAB) standard, employ communication methods based on Orthogonal Frequency Division Multiplexing (OFDM)
In OFDM multiple sub-carrier systems, a higher rate data signal is divided among multiple narrowband sub-carriers that are orthogonal to one another in the frequency domain. Two signals are orthogonal if their dot product is equal to zero. Thus, the higher rate data signal is transmitted as a set of parallel lower rate data signals carried on separate sub-carriers
A received OFDM symbol in an OFDM system generally consists of both data and pilot synchronization information transmitted on the multiple sub-carriers multiplexed together and spanning multiple sample periods Modulation and demodulation in an OFDM system uses an inverse fast Fourier transform (IFFT) at the transmitter and a fast Fourier transform (FFT) at the receiver At the transmitter, a cyclic prefix of a section of the IFFT output for each OFDM symbol is typically appended to the beginning of the OFDM symbol as a guard interval (GI) The length of the OFDM symbol before adding the guard interval is known as the useful symbol period duration. At the receiver, the cyclic prefix is removed prior to the FFT demodulation by the appropriate positioning of an FFT window, which has a size equal to the useful symbol period duration, along a received sample sequence. Subsequently, FFT demodulation transforms the window of received time domain samples, in the received sample sequence, to a frequency domain (OFDM) symbol.
As known to those of skill in the art, OFDM systems can be very sensitive to frequency offsets caused by the mismatch of oscillators in the transmitter and receiver. Another significant source of frequency offset in mobile systems results from the Doppler shift the channel frequency due to the relative motion between the transmitter and receiver
Frequency offset can be divided into an integer portion and a fractional portion as follows:Δƒ=ΔƒI+ΔƒF   (1)The integer portion corresponds to an integral multiple of the sub-carrier spacing that can be represented as:
                    (        2        )                                      Δ          ⁢                                          ⁢                      f            I                          =                              n            I                    ·                      1                          T              u                                          where ΔƒI is the integer frequency offset, nI is the integral multiple and
  1      T    u  is the sub-carrier spacing. Similarly, the fractional portion corresponds to a fractional multiple of the sub-carrier spacing that can be represented as:
                              Δ          ⁢                                          ⁢                      f            F                          =                  Δ          ⁢                                          ⁢                                    f              F              ′                        ·                          1                              T                u                                                                        (        3        )            where ΔƒF is the fractional frequency offset and Δƒ′F is the fractional multiple
The fractional frequency offset destroys orthogonality among sub-carriers, resulting in inter-carrier interference (ICI). While the integer frequency offset does not affect orthogonality, it does cause a circular shift and phase rotation of the received symbols, resulting in a 0.5 bit error rate. Accordingly, the performance of OFDM systems can be improved by using techniques to estimate and compensate for the integer frequency offset.
An example of the basic detection functions of an OFDM receiver is shown in FIG. 1. Conventionally, blocks 101-106 and 108-110 comprise the inner receiver. As will be appreciated, an incoming signal is subject to analog to digital conversion and filtering in block 101 Integer and fractional frequency offset corrections are applied in block 102. Next, the signal is interpolated and decimated in block 103. The GI is removed from the OFDM symbols in block 104 and then the FFT is applied in block 105. Finally, the transformed symbols are equalized and channel estimation is performed in block 106 before the signal is fed to the outer receiver, block 107. Generally, post-FFT estimation routines are performed in block 108 using the output from FFT block 105. The post-FFT routines include determination of the integer portion of the frequency offset, sampling clock estimations and symbol timing estimations. The post-FFT estimations can then be applied to blocks 102, 103 and 104 during reception of subsequent symbols. Transmission mode detection occurs in block 109, typically using autocorrelation of the output of block 103 to determine the transmission mode and GI. Finally, pre-FFT estimation routines are performed in block 110 using the output from block 103 and 109. Preferably, pre-FFT estimations include determination of symbol timing and determination of the fractional portion of the frequency offset
One conventional means of performing the pre-FFT estimation in block 110 involves an autocorrelation routine such as shown in FIG. 2. As one of skill in the art will appreciate, the GI comprises a cyclic prefix such that the set I′ contains the indices of the data samples that are copied to the cyclic prefix and the set I contains the indices of the prefix. Accordingly, the samples in the cyclic prefix and their copies r(t), tεI∪I′ can be pairwise correlated so that:
                              E          ⁢                      {                                          r                ⁡                                  (                  t                  )                                            ·                                                r                  *                                ⁡                                  (                                      t                    +                    N                                    )                                                      }                          =                  {                                                                      E                  ⁢                                                            {                                                                                                                              s                            ⁡                                                          (                              t                              )                                                                                                                                2                                            }                                        ·                                          ⅇ                                                                                                    -                            j2π                                                    ·                          Δ                                                ⁢                                                                                                  ⁢                                                  f                          F                          ′                                                                                                                                                                  t                  ∈                  I                                                                                    0                                            otherwise                                                                        (        4        )            where r(t)=s(t−θ)·ej2πΔƒ′Ft/N+n(t) is received signal and θ is the unknown arrival time of a symbol.
Accordingly, correlation over a window length L between two received signal block, spaced by N samples, can be estimated using a maximum likelihood (ML) method. Specifically, the symbol timing, {circumflex over (θ)}, and fractional portion of the frequency offset, Δ{circumflex over (ƒ)}′F, can be estimated by the following equations:
                              θ          ^                =                  arg          ⁢                                          ⁢                                    max              γ                        ⁢                          {                                                                                                            ∑                                              t                        =                        γ                                                                    γ                        +                        L                        -                        1                                                              ⁢                                                                                  ⁢                                                                  r                        ⁡                                                  (                          t                          )                                                                    ·                                                                        r                          *                                                ⁡                                                  (                                                      t                            +                            N                                                    )                                                                                                                                      -                                  ρ                  ·                                      (                                                                                            1                          2                                                ⁢                                                                              ∑                                                          t                              =                              γ                                                                                      γ                              +                              L                              -                              1                                                                                ⁢                                                                                                          ⁢                                                                                                                                                  r                                ⁡                                                                  (                                  t                                  )                                                                                                                                                    2                                                                                              +                                                                                                                              r                            ⁡                                                          (                                                              t                                +                                N                                                            )                                                                                                                                2                                                              )                                                              }                                                          (        5        )                                          Δ          ⁢                                    f              ^                        F            ′                          =                              -                          1                              2                ⁢                π                                              ⁢                      ∠            ⁡                          (                                                ∑                                      t                    =                                          θ                      ^                                                                                                  θ                      ^                                        +                    L                    -                    1                                                  ⁢                                                                  ⁢                                                      r                    ⁡                                          (                      t                      )                                                        ·                                                            r                      *                                        ⁡                                          (                                              t                        +                        N                                            )                                                                                  )                                                          (        6        )            where the correlation coefficient is
  ρ  =            S      ⁢                          ⁢      N      ⁢                          ⁢      R                      S        ⁢                                  ⁢        N        ⁢                                  ⁢        R            +      1      Further details of this method are described in van de Beek, et al, ML Estimation of Time and Frequency Offset in OFDM Systems, IEEE Transactions On Signal Processing, 45:7 (July 1997), which is hereby incorporated by reference in its entirety.
Following the pre-FFT estimation routines in block 110, the residual fractional portion of the frequency offset is relatively small. In turn, the post-FFT estimation occurring in block 108 using these values has relatively little ICI noise The effect of these routines means that the k'th transmitted subcarrier arrives at the FFT output bin with an index of k=k′+nI.
Conventionally, the spectral shift is determined next. Since n1=Δƒ1·Tu, the symbol demodulated by the FFT routine, corresponding to the Ith OFDM symbol on the subcarrier k, can be represented represented as:Zl,k=al,k′Hl,k′·ej2π((l(N+L)+L)/N)nI+nl,k   (7)where al,k′ is the transmitted symbol at subcarrier k′ and OFDM symbol I and Hl,k′ is the channel transfer function at subcarrier frequency k′.
In OFDM systems employing continuous pilots (CP), the spectral shift nI can be detected using the CPs ck′ at specified subcarrier positions k′εC. For example, in the DVB-T standard, the transmitted CPs are boosted in power by factor β2 and modulated using time-invariant symbols. Using the techniques described above, correlating FFT output symbols of two consecutive OFDM symbols I-1 and I, and assuming that Hlk≈Hl−l,k, leads to the following equation:
                              x          k                =                                            z                              l                ,                k                                      ·                          z                                                l                  -                  1                                ,                k                            *                                =                                                    ⅇ                                                      j2π                    ⁡                                          (                                                                        (                                                      N                            +                            L                                                    )                                                /                        N                                            )                                                        ·                                      n                    I                                                              ·                                                                                      H                    k                                                                    2                            ·                              {                                                                                                    β                        2                                                                                                            k                        ∈                                                  C                          +                                                      n                            I                                                                                                                                                                                                                            a                                                      l                            ,                                                          k                              ′                                                                                                      ·                                                  a                                                                                    l                              -                              1                                                        ,                                                          k                              ′                                                                                *                                                                                                                                    k                        ∈                                                  B                          +                                                      n                            I                                                                                                                                                                          0                                                              otherwise                                                                      }                                      +            noise                                              (        8        )            where B is the set of transmitted non-CP samples, for example transmission parameter signaling (TPS), scattered pilots (SP), and data, appearing at random. Accordingly, the estimated spectral shift {circumflex over (n)}I is
                                          n            ^                    I                =                  arg          ⁢                                          ⁢                                    max                              m                ∈                Γ                                      ⁢                                                                                                ∑                                          k                      ∈                                              C                        +                        m                                                                                                                                            ⁢                                                                          ⁢                                      x                    k                                                                              ⁢                              ∀                                  m                  ∈                  Γ                                                                                        (        9        )            where Γ is the search range given by └−nI,max, nI,max┘ Further, the integer frequency offset can also be estimated as
      Δ    ⁢                  f        ^            I        =                    n        ^            I        ·                  1                  T          u                    .      
Similar conventional techniques can be used to estimate the integer portion of the frequency offset in OFDM symbols that employ scattered pilots as well. As will be recognized, FIG. 3 depicts the frame structure of a DVB-T system that uses scattered pilots This frame structure is also similar to that employed by ISDB-T systems In the embodiment shown, the scattered pilot values are transmitted at a rate of every 12 sub-carrier frequencies. When the OFDM symbol index p=mod(l,4) is unknown, four possible SP patterns {S0, S1, S2, S3} exist, as shown in FIG. 3. Because the SP patterns repeat every four OFDM symbols, the autocorrelation at the FFT output of samples from OFDM symbols I-4 and I assuming Hl,k≈Hl-4,k is given as
                              x          k                =                                            z                              l                ,                k                                      ·                          z                                                l                  -                  4                                ,                k                            *                                =                                                    ⅇ                                                      j2π                    ⁡                                          (                                              4                        ⁢                                                                              (                                                          N                              +                              L                                                        )                                                    /                          N                                                                    )                                                        ·                                      n                    I                                                              ·                                                                                      H                                          k                      ′                                                                                        2                            ·                              {                                                                                                    β                        2                                                                                                            k                        ∈                                                                              S                                                          mod                              ⁡                                                              (                                                                  l                                  ,                                  4                                                                )                                                                                                              +                                                      n                            I                                                                                                                                                                                                                            a                                                      l                            ,                                                          k                              ′                                                                                                      ·                                                  a                                                                                    l                              -                              4                                                        ,                                                          k                              ′                                                                                *                                                                                                                                    k                        ∈                                                  H                          +                                                      n                            I                                                                                                                                                                          0                                                              otherwise                                                                      }                                      +            noise                                              (        10        )            where {circumflex over (p)} is the estimated symbol index {circumflex over (p)}ε{0,1,2,3}, Smod(l,4) is the set of SP transmitted at symbol I, and H is the set of transmitted non-SP samples, for example, TPS, CP and data. For example, as shown in FIG. 3, autocorrelation can be performed between SP values 301 and 302.
As one of skill in the art will recognize, these prior art methods for determining the integer portion of the frequency offset and symbol timing suffer from certain drawbacks. In schemes employing continuous pilots, the pilots occupy a significant fraction of the signal, limiting the efficiency of the system. For example, there are 177 CPs in the 8K mode and 45 CPs in the 2K mode in conventional DVB-T systems. Accordingly, the pilots consume a significant portion of the overall signal and therefore it would be desirable to employ systems that do not require CPs.
The prior art methods also suffer limitations in systems using scattered pilots, such as one-segment ISDB-T. As discussed above, determination of the integer frequency offset requires the assumption that Hl,k≈Hl-4,k so that the autocorrelation determination can be made. However, when the channel is time varying, then Hl,k′≠Hl−4,k′ preventing use of the methods discussed above. Moreover, even if the channel is not time varying, interference between the sub-carriers can interfere with autocorrelation, also preventing the use of these prior art methods.
Accordingly, it would be desirable to provide systems and methods that allow determination of the integer frequency offset and symbol timing without autocorrelation. It would also be desirable to provide systems and methods for determining the integer frequency offset and symbol timing without requiring continuous pilots. Finally, it would be desirable to provide such systems and methods that optimize the efficiency of an OFDM system and offer improved performance in mobile applications.